6 CLAUS1U8 OX THE MECHANICAL EQUIVALENT 



must be introduced into the calculation as an increase of the 

 vis viva ; and now let us turn to the consideration of electricity. 

 There can exist no doubt that the equation (2), which referred 

 originally to the motions oi material masses, is also applicable to 

 the electricity within these masses ; a statement already made in 

 a very general manner by Helmholtz, and partly established*. 



To give, however, the quantity -'^mv^, which appears in this 



equation, a meaning so general as to embrace the motion both 

 of the material masses and of the electricity, we must, in the 

 first place, decide whether the electricity is subject to the laws 

 of inertia, so as to permit of vis viva being ascribed to it. This 

 question is manifestly of the greatest importance to the whole 

 science of electricity \ notwithstanding this, however, we will 

 not enter upon its discussion here, inasmuch as its solution is 

 without influence upon the present investigation. 



If the work produced by the electricity in any change of 

 arrangement whatever be compared with the cases already cited, 

 we readily observe that it is included in the last of these cases, 

 inasmuch as in the production of this work the forces in action 

 consist only in the mutual attraction or repulsion of the par- 

 ticles of electricity, this being inversely proportional to the 

 square of the distance. From this it immediately follows, 

 that the said work is independent of the manner in ivhich the 

 alteration is effected, and depends only on the primitive and final 

 conditions, and that the work is measured by the increase of the 

 potential of the entire electricity upon itself ■\, 



* Ueher die Erhaliung der Kraft (On the Conservation of Force), a physical 

 memoir by Dr. H. Helmholtz. Berlin bei G. Reimer, 1847. It is to be re- 

 gretted that the author of this ingenious essay has not entered more fully into 

 the details of his subject. From this cause certain portions appear to me to 

 be inexact, and others difficult to be understood ; such a mass of thought it 

 would, however, be difficult to press into a narrow space, [The memoir here 

 referred to will appear in the next Part of this work. — Eds.] 



t Helmholtz gives in a case cited by him as an example (see p. 40) the fol- 

 lowing expression for the work produced : 



-{v^^^y 



while, with the same meaning attached to the letters, the increase of the poten- 

 tial is 



-(V+W„-f-Wft). 

 This divergence from the above proposition is simply due to the fact that he 



